The key issue is to enter the initial Mathematica construction correctly. That is done as follows.

The $\bot$ character is Mathematica's symbol \[UpTee] which is interpreted as the UpTee function which takes two arguments. This is part of the cause of the error messages you got. You haven't provided those.

You can type Esc+null+Esc for the first argument (which is nothing thanks to the null), followed by Esc+uT+Esc and Esc+null+Esc again for the second argument.

The same goes for the $\parallel$ character, Mathematica's DoubleVerticalBar symbol and (undefined) function which can be entered as Esc+Space+||+Esc.

to generate your TeX code. If you want square brackets you may want to change the \left( to \left[ and \right( to \right[. Additionally, since Mathematica interprets E as Euler's number it ends up as a lower case e in the TeX code. You may want to change that back to an uppercase E manually afterwards, or use a \[CapitalEpsilon] in Mathematica. This gets translated as E in the TeX code.

Mathematica is a registered trademark of Wolfram Research, Inc. While the mark is used herein with the limited permission of Wolfram Research, Stack Exchange and this site disclaim all affiliation therewith.